Dependence of Exciton Diffusion Length on Crystalline Order in

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Dependence of Exciton Diffusion Length on Crystalline Order in Conjugated Polymers Myungsun Sim, Sae Byeok Jo, Jisoo Shin, Min Kim, Chiyeoung Shim, Joo-Hyun Kim, and Kilwon Cho J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 23 Dec 2013 Downloaded from http://pubs.acs.org on December 23, 2013

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The Journal of Physical Chemistry

Dependence of Exciton Diffusion Length on Crystalline Order in Conjugated Polymers

Myungsun Sim, Jisoo Shin, Chiyeoung Shim, Min Kim, Sae Byeok Jo, Joo-Hyun Kim, and Kilwon Cho*

Department of Chemical Engineering, Pohang University of Science and Technology, Pohang, 790−784, Korea

* To whom all correspondence should be addressed. E-mail: [email protected]

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Abstract Exciton diffusion in organic semiconductors is crucial to the performance of organic solar cells. Here, we measured the exciton diffusion length in poly(3-hexylthiophene) (P3HT)

as a function

of the

crystalline

order using spectrally

resolved

photoluminescence quenching (SR-PLQ) techniques. The crystalline order in the P3HT films, characterized according to the mean crystal size and normalized crystallinity, was varied by changes in thermal treatment temperatures. The exciton diffusion length increased from 3 nm to 7 nm as the mean crystal size increased more than twice and the crystallinity increased by a factor of six. A higher crystalline order improved the spectral overlap and reduced the distance between chromophores, enhancing Förstermediated exciton diffusion. The higher crystalline order also lengthened the conjugated segments and reduced the energetic disorder, producing favorable condition for exciton hopping.

Keywords: conjugated polymer, crystalline order, chromophore size distribution, spectral overlap, energetic disorder, and exciton diffusion length

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Introduction In recent years, polymer solar cells have been extensively studied as low cost alternative energy sources. The power conversion efficiency of a polymer solar cell exceeded 8%:1 however, further increases are limited in part by the very short exciton diffusion lengths (LD) in organic semiconductors. The exciton diffusion length in an organic semiconductor is typically much smaller than the optical absorption length. Extending the exciton diffusion length is an important consideration toward optimizing the design of polymer solar cells.2-5 Exciton diffusion in conjugated polymers has been less extensively studied than that in small molecules.6-18 Small conjugated molecules are amenable to thicknessdependent photoluminescence (PL) quenching techniques used to measure the LD values, because the film thickness may be tuned using evaporation deposition.6,19 However, conjugated polymers are not suitable for this technique because polymer films are usually deposited by a solution process that is not amenable to the formation of continuous thin films several nanometers in thickness. Most of the studies on exciton diffusion length in organic semiconductors have focused on measurement methods rather than on the correlations between the material properties and the LD values.9,20-23 Recently, Forrest reported the relationship between the crystalline order and the exciton diffusion length in small molecule semiconductors.24 However, this study is not directly applicable to conjugated polymer systems because exciton diffusion in a conjugated polymer differs from that in a small molecule films. Unlike the small molecule semiconductors, conjugated polymers include a distribution of chromophore sizes.25 A conjugated polymer chain consists of conformational subunits separated by conjugation breaks caused by twists or kinks in 3



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the backbone chain. A conformational subunit acts as an effective chromophore, that is, a light-absorbing unit, in which electronic excitation is localized after photoexcitation. The chromophore size distribution in a conjugated polymer film is affected by the crystalline order which can be easily controlled by varying the processing conditions, such as the coating process or the application of post-treatments. Thermal treatments are widely used to enhance the performances of polymer optoelectronic devices. Thermally treated polymer semiconductors display greater crystalline orderings, which improves the light absorption and charge transport.26-29 The size and spatial distributions of the chromophores can vary with the crystalline order. Such properties affect exciton diffusion because excitons migrate by hopping between chromophores. Here, we investigated the effects of the crystalline order on the exciton diffusion lengths in poly (3-hexylthiophene) (P3HT) films. The degree of crystalline order in a P3HT film was controlled by thermal treatment. The exciton diffusion lengths were measured using spectrally resolved photoluminescence quenching (SR-PLQ) method,22 which had been modified for application to soluble polymer systems. The exciton diffusion lengths in P3HT increased with the crystalline domain size and crystallinity. A higher crystalline order improved the spectral overlap and reduced the distance between chromophores, enhancing Förster-mediated exciton diffusion. The higher crystalline order also lengthened the conjugated segments and reduced the energetic disorder, both of which improvements tended to favor exciton hopping. Experimental Section Regioregular P3HT (4002-E) samples were purchased from Rieke Metals Inc. Thick P3HT films were spin-coated in chloroform or chlorobenzene solvents in a glove 4


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box under a nitrogen atmosphere. The film thickness was about 250 nm. The films were thermally treated, then cooled slowly. The crystalline order was determined by the thermal treatment temperature, which was varied over the range 180-235°C. The crystalline orders of the as-cast and annealed films were characterized by grazing incidence X-ray diffraction (GIXD). The full width of half maximum (FWHM) and d-spacing of the (100) diffraction peak were analyzed by 1-dimensional (1D) GIXD experiments in both the out-of-plane and in-plane configurations and the molecular orientations and angular integrated diffraction peaks were analyzed by 2-dimensional (2D) GIXD experiments. The morphologies of the films were characterized by AFM (Digital Instruments Multimode) operated in the tapping mode. SR-PLQ measurements were carried out in a spectrofluorometer (Jasco). The excitation spectra of the P3HT films containing polyvinylpyrrolidone (PVP) blocking or TiOX quenching layers were collected over the range λ=400–600 nm at a peak emission wavelength of 650 nm. The thicknesses of the PVP and TiOx layers were about 30 nm. An exciton blocking layer was found to be necessary to avoid exciton quenching at the free P3HT surface. The degree of PL quenching, η, was calculated as the ratio of the excitation spectrum intensity in the sample prepared with a blocking layer (PLB) to the intensity in an equivalent sample prepared with a quenching layer (PLQ). The excitation spectra were corrected for transmission losses and reflectance variations in the quenching and blocking layers, as measured using the spectrophotometers. The absorption coefficients were calculated by dividing the absorbance acquired using the spectrophotometer (Varian, CARY-5000) by the film thickness determined using an ellipsometer (M-200V, H. A. Woollam Co., Inc.) and corroborated by AFM measurements. Modified absorption coefficients (α’) were 5



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obtained by adjusting the absorption coefficients (α) for the incidence illumination angle (θλ): α’=α/cosθλ. The θλ was 60°. Energy transfer to the quenching layer was negligible because the TiOX band gap was large; therefore, η was related to the LD values extracted according to: η = α’LD +1.22 The error bars on the diffusion length were propagated from the uncertainty in the PL measurements for each sample and from the errorweighted least squares fitting. Results and Discussion The extent of crystalline order in the P3HT films was varied according to thermal treatment temperatures and characterized by GIXD, as shown in Figure 1 and summarized in Table 1. The film thermally annealed at 235°C formed a meltcrystallized film with the highest degree of crystallinity observed in this data set. The positions of (100) and (010) diffraction peaks of the films were slightly shifted so that the d-spacing of the (100) and (010) planes decreased slightly as the thermal treatment temperature increased.

The

intensity (brightness) of the diffraction image,

corresponding to the (100), (200), and (300), and (010) peaks of the P3HT films, increased as the thermal treatment temperature increased. The relative degree of the P3HT crystallinity (N) was quantitatively determined as a function of the thermal treatment temperature by measuring the angular–integrated intensity of the (100) diffraction peak because the GIXD data showed the (100) diffraction peak was the most dominant peak compared to other diffraction peaks. The intensity of each film was then normalized by the intensity of the melt-crystallized film. This relative degree of crystallinity (N) increased with the thermal treatment temperature, suggesting that the P3HT chains became more mobile and shifted to positions that were more

6


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thermodynamically-stable resulting in a larger number of crystallites. The N value of the melt-crystallized film was six times larger than that of the as-cast film. The diffraction peaks narrowed as the thermal treatment temperature increased. The narrowing of the diffraction peaks indicated an increase in the coherent domain size which could be estimated using the Scherer equation, given by R=

K ⋅λ FWHM ⋅ cos θ

(1)

where K is the dimensionless Scherrer constant, λ is the incident X-ray wavelength, FWHM is the full width at half maximum of the peak, and θ is the Bragg angle. The stacking distances and coherent domain sizes of the (100) and (010) peaks for the thermally annealed samples are given in Table 1. The (100) and (010) coherent domain sizes increased with the thermal treatment temperature, suggesting that the stacking defects decreased and the intrachain/interchain ordering increased. The (100) coherent domain size of the melt-crystallized film was more than twice larger than that of the ascast film. Instrumental broadening effects were not considered here. The instrumental broadening was expected to remain constant and provide a negligible effect relative to the sample broadening.30 This allowed the sample features to be compared directly. The P3HT film surfaces were observed by AFM. Figure 2 shows that the morphological feature of the P3HT crystal became clearer and the P3HT crystal domain size seemed to increase as the thermal treatment temperature increased. P3HT films are polycrystalline films containing randomly oriented crystal domains. The meltcrystallized P3HT film prepared at 235°C displayed a nanofibrillar structures with a width of 20–40 nm and a length of several µm (Figure 2c). The width and length of the P3HT nanofiber are related to the crystal domain sizes along the (001) and (010) directions, respectively.31 The (001) and (010) crystal domain sizes of the melt7



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crystallized film were dramatically increased, compared to those of as-cast film. As shown in Figure 2c, the real (010) crystal domain size of the melt-crystallized film could be much larger than the coherent domain size obtained by GIXD (Table 1) because the coherent domain sizes were estimated using the Scherer equation based on a spherical shape crystal which is not accurate for a fibrillar crystal. Furthermore, the (010) diffraction peak was observed in high angle region where the diffraction peak has a relatively low resolution due to geometric effects, compared to the diffraction peak in low angle region. However, as deduced from AFM and GIXD results, it is clear that the crystal size in the P3HT film increased in all directions as the thermal treatment temperature increased. The exciton diffusion lengths were measured as a function of the thermal treatment temperature (which modulated the extent of crystalline order) using the SRPLQ technique,22 as shown in Figure 3. The degree of PL quenching (η) varies linearly with the modified absorption coefficient with incident illumination angle (θλ): η = (α/cosθλ)LD +1 = α’LD +1, which was obtained by solving the one-dimensional steady state exciton diffusion equation for the thick P3HT film.22 As shown in Figure 3c, the slope of a plot of η versus α’ then yields the exciton diffusion length, LD. As the thermal treatment temperature increased, both the α’ value and the η value increased (Figure 3a and 3b); however, the α’ value increased to a lesser degree than the η value. As a result, the exciton diffusion length increased as the thermal treatment temperature increased (Figure 3c). As shown in Table 1, the exciton diffusion length increased as the crystalline order increased. The exciton diffusion length increased from 3 nm to 7 nm as the mean crystal size in case of simple cubic P3HT crystal increased more than twice and the 8


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relative degree of crystallinity increased by a factor of six. Figure 4 shows the relationship between exciton diffusion length and the relative degree of crystallinity (N). The exciton diffusion length increased dramatically at the low crystalline order and became saturated at the high crystalline order. The diffusion length trends in P3HT were further explored by considering line dipole approximation and the weak dipole–dipole coupling limit, in which strong exciton–phonon interactions produce random exciton hopping behaviors.32 In this case, line-dipole Förster-type energy transfer rate was used to describe singlet exciton hopping via33,34

k DA

 2π =  h

Φ  2 VDA J ≈ F 4 τ  Dn

2

 N   ∑ Ψk Γkl rDA −3 Ψl  J ,  k ,l 

(2)

1 rDA

(3)

and VDA ∝

where VDA is the electronic coupling between the donor and acceptor chromophores, Γ is the dipole orientation factor, n is the refractive index, J is the spectral overlap integral between the emission spectrum of the donor chromophore and the absorption spectrum of the acceptor chromophore, ΦF is the fluorescence yield, rDA is the average hopping distance between a donor chromophore and an acceptor choromophore, and τD is the fluorescence lifetime of the donor chromophore. To get more insights of exciton diffusion lengths, we have discussed the effects of each parameter on the LD in Eq. (2). The dipole factor for a crystalline material is, Γ = cos(θAD) – 3cos(θA)cos(θD), where θAD is the angle between the donor and acceptor dipole moments, and θA and θD are the angles between the molecular stacking direction 9



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and the dipole moment of the donor (D) and acceptor (A) chromophore pairs.22 We assumed that Γ changed negligibly with the crystalline ordering because of random polymer conformations and spatial distributions of chromophores. The value of n in a P3HT film was not expected to change much with the degree of crystalline order because n is a material property of the material itself. The fluorescence yield, ΦF, is the ratio between the number of photons emitted through fluorescence and the number of photons absorbed by a chromophore. In case of large grains in molecular organic semiconductors, the number of photons emitted through fluorescence increases by reducing nonradiative exciton loss at grain boundaries. The fluorescence quantum yield of 3,4,9,10-perylenetetracarboxylic dianhydride, a polycrystalline small molecule, was previously found to increase with the grain sizes.24 Unlike small molecule semiconductors, the chromophore size (effective conjugation length) in a polymer chain can be enlarged by thermal treatments, which results in an increase of the transition dipole moments of the chromophores and thus the enhancement of the absorption coefficients.32 As shown Figure 3a, thermal treatments of a P3HT film increased the absorption coefficient of P3HT and thus the number of photons absorbed by the P3HT film. The fluorescence quantum yield, ΦF, was not expected to vary with the degree of crystalline order in the P3HT films (Table T1 in the Supporting Information). The spectral overlap integral, J, quantifies the overlap between the normalized donor fluorescence and acceptor absorption spectra,35,36 according to:

J = ∫ FD (λ ) AA (λ )λ4 dλ .

(4)

J could not be obtained from the thick P3HT films studied here because the chromophores in the P3HT films were characterized by a size distribution. It was 10


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experimentally impossible to obtain the fluorescence and absorption spectra of each chromophore and calculate J exactly for each chromophore; however, the J values for each P3HT film could be qualitatively estimated based on a film’s static fluorescence and absorption spectral overlap integrals. The static spectrum of a film is the sum of the spectra of each chromophore in the film. Figure 5 shows the normalized absorption and fluorescence spectra for as-cast and thermally annealed P3HT films. An increase in the coherent domain size and relative degree of crystallinity in the conjugated polymers was correlated with a decrease in the number of defect sites and an increase in the intra/interchain order. High intra/interchain order indicated that the chains within each aggregate domain assumed a more rigid and planar form.37 Therefore, the main absorption peaks for the P3HT films were red-shifted from 505 nm to 514 nm, and the shoulder peaks at around 550 nm and 600 nm became more pronounced as the thermal treatment temperature increased. The fluorescence spectrum became slightly blueshifted as the thermal treatment temperature increased because the high intra/interchain order hinders the torsional relaxation in the excited conjugated segments prior to fluorescence.25,38,39 As a result, the overlap integral between the fluorescence and absorption spectra increased as the degree of crystalline order increased. This result suggested that J between the chromophore increased on average as the degree of crystalline order increased. This larger spectral overlap integral increased the Förster radius, R0, and promoted exciton migration. As the degree of crystalline order increased, the P3HT chain packing became more compact, as shown in Table 1. The lattice constants for the (100) and (010) planes decreased slightly as the thermal treatment temperature increased, and the P3HT film thickness decreased slightly. These results indicated that the P3HT chain packing 11



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density increased, bringing the chromophores closer to one another. As shown in Eq. (2) and (3), the exciton diffusion length depends on the average hopping distance, rDA, according to an inverse 2nd power law. Exciton diffusion may, therefore, be enhanced in thermally treated films characterized by a high chain packing density. These results were consistent with the experimentally observed increase in exciotn migration in going from a solution to a solid state due to the emergence of channels that promote hopping between chains in close contact.32,40 An increase in the average effective conjugation length with the thermal treatment temperature also enhanced exciton diffusion. The conjugation length of a polymer is closely related to the exciton bandwidth (W) induced by interchain interaction. The exciton bandwidth decreases as the conjugation length increases when the conjugation length is longer than the intermolecular separation according to quantum chemical calculations.41,42 The exciton bandwidth can be quantitatively estimated form the ratio of the 0-0 transition and 0-1 transition peaks in the absorption spectrum (Figure 5) according to the expression: 42-44 A0 −0 (1 − 0.24W / ω 0 ) 2 . ≈ A0−1 (1 + 0.073W / ω 0 ) 2

(5)

where ω0 is the intramolecular vibration frequency. Equation (5) shows that a lower exciton bandwidth is expected for a higher ratio between the intensity of the 0-0 transition (A0-0) and that of the 0-1 transition (A0-1). The values of A0-0 and A0-1 were obtained from fits to the absorption spectrum (Figure S2 in the Supporting Information). Table 2 reveals that the values of exciton bandwidth W/ω0 decreased as the thermal treatment temperature increased. This suggested that the average effective conjugation length (chromophore size) in the polymer chains increased with the thermal treatment temperature. Thermally activated exciton hopping between large chromophores can be 12


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more effective than that between small chromopores because it requires the fewer number of hops.45,46 Therefore, larger chromophores can enhance the exciton diffusion length. Energetic disorder can reduce the exciton diffusion length.47,48 Variations in the molecular conformation or size of conjugated segments (especially in conjugated polymers), inhomogeneities in the intermolecular interactions, chemical defects, or impurities lead to a Gaussian distribution of the HOMO–LUMO energy gaps – and the excitonic energies. Excitons undergo random walk migration (diffusion) among energy sites (conjugated segments) via energy transfer. The half-width σ of the Gaussian distribution of the energy sites is a measure of the site–energy disorder, and the exciton diffusion length can increase as σ decreases. We estimated the half-widths σ from the exciton bandwidth W and the ratio (I0-0/I0-1) of the 0-0 to 0-1 emission peaks (Figure 5 and Figure S3 in the Supporting Information) using a simplified expression of Spano’s model,42,43 I 0−0 (1 − 0.24W / ω 0 ) 2 σ 2 . ≈ −2 I 0 −1 2e (1 − 0.39W / ω 0 ) 2 W 2

(6)

This expression is expected to be valid under conditions of spatially uncorrelated disorder, with a Huang–Rhys factor of λ2=1. Equation (6) suggests that a lower exciton bandwidth and/or higher disorder are expected if 0-0 emission bands are more intense than the 0-1 emission bands. As shown in Table 2, the disorder (σ/ω0) decreased as the thermal treatment temperature increased, suggesting that the thermal–treatment–induced crystalline order reduced site energy disorder, thereby increasing the exciton diffusion length.

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Conclusions We investigated the effects of crystalline order on the exciton diffusion length in a P3HT film. The crystalline order of a P3HT film was determined based on the mean crystal size and the normalized crystallinity, which increased with thermal treatment temperature. The exciton diffusion length was measured using a modified SR-PLQ method. The exciton diffusion length increased from 3 nm to 7 nm as the mean crystal size increased more than twice and the crystallinity increased by a factor of six. The increase in P3HT crystalline order improved the spectral overlap integral between the donor fluorescence and acceptor absorption and brought the chromophores closer to one another, thereby enhancing Förster-mediated exciton diffusion. The higher crystalline order favored the formation of longer conjugated segments and reduced the energetic disorder, producing favorable condition for exciton hopping. In summary, a higher crystalline order improved the exciton diffusion length in P3HT films. This result will contribute to the understanding of exciton diffusion in polymer solar cells.

Acknowledgements This work was supported by a grant (Code No. 2011-0031628) from the Center for Advanced Soft Electronics under the Global Frontier Research Program of the Ministry of Education, Science and Technology, Korea.

Supporting Information Available: Rocking-curve on the (100) diffraction peak, fluorescen quantum yield, and analysis of absorption and fluorescence spectra. This material is available free of charge via the internet at http://pubs.acs.org

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Table 1.

Lattice constants, mean crystal sizes, normalized angular-integrated

intensities, and exciton diffusion lengths for the P3HT crystallites in as-cast and thermally treated films.

Table 2.

The 0-0 to 0-1 peak intensity ratio from the absorption and emission spectra,

the exciton band widths (W/ω0) and the disorder parameters (σ/ω0) for the as-cast and thermally treated P3HT films.

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Figure captions Figure 1. 2D GIXD patterns for (a) an as-cast P3HT film and thermally treated P3HT films at (b) 180°C and (c) 235°C.and (d) Angular-integrated diffraction patterns of the films.

Figure 2. AFM images and height profiles of (a) an as-cast P3HT film and thermally treated P3HT films at (b) 180°C and (c) 235°C.

Figure 3. Measurement of P3HT diffusion length using spectrally resolved photoluminescence quenching. (a) Modified absorption coefficients for the non-normal incidence (α’); (b) the degree of luminescence quenching (η) versus wavelength; and (c) η versus α’ for the as-cast (■) and thermally treated films at 180°C (●) and 235°C (▲); (d) Schematic diagram of the sample structures and measurement system used for the exciton diffusion analysis.

Figure 4. Exciton diffusion length versus the relative degree of crystallinity (N) for the P3HT film. Figure 5. Normalized absorption (left) and fluorescence (right) spectra of the as-cast (■ and □) and thermally treated P3HT films at 180°C (● and ○) and 235°C (▲and △).

20


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Figure 1.

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Figure 2.

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Figure 3.

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Figure 4.

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Figure 5.

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Table of Contents Image

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Dependence of Exciton Diffusion Length on Crystalline Order in

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